We consider fractional NLS with focusing power-type nonlinearity $$i \partial_t u = (-\Delta)^s u - |u|^{2 \sigma} u, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^N,$$ where $1/2 < s < 1$ and $0 < \sigma < \infty$ for $s \geq N/2$ and $0 < \sigma \leq 2s/(N-2s)$ for $s < N/2$. We prove a general criterion for blowup of radial solutions in $\mathbb{R}^N$ with $N \geq 2$ for $L^2$-supercritical and $L^2$-critical powers $\sigma \geq 2s/N$. In addition, we study the case of...

Topics: Analysis of PDEs, Mathematics, Mathematical Physics

Source: http://arxiv.org/abs/1509.08845

"Index bibliographique": p. [xvii]-xix

Topics: Julian, Emperor of Rome, 331-363, Greek language, Greek language, Hellenistic (300 B.C.-600 A.D.)